Base field \(\Q(\zeta_{36})^+\)
Generator \(w\), with minimal polynomial \(x^{6} - 6x^{4} + 9x^{2} - 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[1, 1, 1]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 9x^{2} + 12\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 8 | $[8, 2, w^{3} - 3w - 1]$ | $\phantom{-}e^{3} - 6e$ |
| 37 | $[37, 37, w^{4} - 5w^{2} - w + 5]$ | $-2e^{2} + 8$ |
| 37 | $[37, 37, w^{5} - 5w^{3} - w^{2} + 4w + 1]$ | $-2e^{2} + 8$ |
| 37 | $[37, 37, -w^{5} + w^{4} + 5w^{3} - 4w^{2} - 5w + 1]$ | $-2e^{2} + 8$ |
| 37 | $[37, 37, w^{5} + w^{4} - 5w^{3} - 4w^{2} + 5w + 1]$ | $-2e^{2} + 8$ |
| 37 | $[37, 37, w^{5} - 5w^{3} + w^{2} + 4w - 1]$ | $-2e^{2} + 8$ |
| 37 | $[37, 37, -w^{4} + 5w^{2} - w - 5]$ | $-2e^{2} + 8$ |
| 71 | $[71, 71, w^{5} - 5w^{3} - w^{2} + 5w + 4]$ | $-e^{3} + 3e$ |
| 71 | $[71, 71, w^{5} - 4w^{3} - w^{2} + w + 2]$ | $-e^{3} + 3e$ |
| 71 | $[71, 71, w^{5} + w^{4} - 5w^{3} - 5w^{2} + 4w + 2]$ | $-e^{3} + 3e$ |
| 71 | $[71, 71, w^{5} - w^{4} - 5w^{3} + 5w^{2} + 4w - 2]$ | $-e^{3} + 3e$ |
| 71 | $[71, 71, -w^{5} + 4w^{3} - w^{2} - w + 2]$ | $-e^{3} + 3e$ |
| 71 | $[71, 71, -w^{5} + 5w^{3} - w^{2} - 5w + 4]$ | $-e^{3} + 3e$ |
| 73 | $[73, 73, w^{5} - 5w^{3} - w^{2} + 3w + 2]$ | $\phantom{-}e^{2} - 4$ |
| 73 | $[73, 73, 2w^{5} - w^{4} - 10w^{3} + 4w^{2} + 9w - 2]$ | $\phantom{-}e^{2} - 4$ |
| 73 | $[73, 73, -w^{5} + 4w^{3} - w^{2} - 2w + 2]$ | $\phantom{-}e^{2} - 4$ |
| 73 | $[73, 73, w^{5} - 4w^{3} - w^{2} + 2w + 2]$ | $\phantom{-}e^{2} - 4$ |
| 73 | $[73, 73, -2w^{5} - w^{4} + 10w^{3} + 4w^{2} - 9w - 2]$ | $\phantom{-}e^{2} - 4$ |
| 73 | $[73, 73, w^{5} - 5w^{3} + w^{2} + 3w - 2]$ | $\phantom{-}e^{2} - 4$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).